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We have deduced a two-level form of beam evolution in photonic lattices of semiconductor photorefractive medium and its classical canonical form of the two-level equation. We analytically calculate the fixed points of the classical canonical aligns, analyze its stability and calculate the critical value of topology changes. According to the classical canonical form of the two-level equation, we make space phase diagram, further analyze the self-trapping of beam propagation in semiconductor photorefractive medium and find two kinds of self-trapping: 1) Both the population difference and the relative phase in energy levels oscillate near an equilibrium point in the phase space. 2) The population difference in energy levels oscillate near an equilibrium point while the relative phase increases monotonously. From the three aspects of high frequency, low frequency, and intermediate frequency, we investigate how an external periodic field influences the self-trapping and find that the external high frequency periodic field may dramatically modulate the critical points at which the transition to self-trapping occurs. It makes the self-trapping occur with small nonlinear effect when the beam propagates in semiconductor photorefractive medium.
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Keywords:
- semiconductor photorefractive medium /
- self-trapping /
- two-level form /
- periodic modulation
[1] Ashkin A, Boyd G D, Dziedzic J M, Smith R G, Ballman A A, Levinstein J J, Nassau K 1966 Appl. Phys. Lett. 40 72
[2] Wang X D, Yu W L 2011 Acta Scientiarum Naturalium Universitatis Sunyatseni 40 32 (in Chinese) [王晓东, 佘卫龙 2011 中山大学学报: 自然科学版 40 32]
[3] Ren Z M 2005 Laser Journal 26 1 (in Chinese) [任占梅, 激光杂志 2005 26 1]
[4] Hou C F, Li S Q, Li F, Sun X D 2001 Progress In Physics 21 237 (in Chinese) [侯春风, 李师群, 李斌, 孙秀冬 2001 物理学进 21 237]
[5] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 3699 (in Chinese) [王沙, 杨志安 2009 物理学报 58 3699]
[6] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 729 (in Chinese) [王沙, 杨志安 2009 物理学报 58 729]
[7] Hu Y, Lou C B, Liu S, Zhang P, Zhao J L, Xu J J, Chen Z G 2009 Opt. Lett. 34 1114
[8] Hu Y, Lou C B, Zhang P, Xu J J, Yang J K, Chen Z G 2009 Opt. Lett. 34 3259
[9] Zhang P, Liu S, Zhao J L, Lou C B, Xu J J, Chen Z G 2008 Opt. Lett. 33 878
[10] Chen S M, Shi S X, Dong H Z 2005 Acta Phys. Sin. 56 1379 (in Chinese) [陈守满, 石顺祥, 董洪舟 2005 物理学报 56 1379]
[11] Wang D S, Yu W L 2007 Acta Phys. Sin. 56 245 (in Chinese) [汪德生, 佘卫龙 2007 物理学报 56 245]
[12] Wang X S, Chen Z G, Wang J D, Yang J K 2007 Phys. Rev. Lett. 99 243901
[13] Ghulinyan M, Oton C J, Gaburro Z, Pavesi L T C, Wiersma D 2005 Phys. Rev. Lett. 94 127401
[14] Liu J, Fu L B 2010 Phys. Rev. A 81 1114
[15] Song D Y 2000 Phys. Rev. 85 1141
[16] Zhu S L, Wang Z D 2000 Phys. Rev. Lett. 85 1076
[17] Li S C, Liu J, Fu L B 2011 Phys. Rev. A 83 042107
[18] Wang G F, Liu F, Fu L B, Zhao H 2007 Acta Phys. Sin. 56 3733 (in Chinese) [王冠芳, 刘斌, 傅立斌, 赵鸿 2007 物理学报 56 3733]
[19] Ye D F, Fu L B, Zhao H, Liu J 2007 Acta Phys. Sin. 56 5071 (in Chinese) [叶地发, 傅立斌, 赵鸿, 刘杰 2007 物理学报 56 5071]
[20] Zener C 1932 Proc. R. Soc. London A 137 692
[21] Landau L 1932 Phys. Z. Sowjetunion 2 46
[22] Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 2661 (in Chinese) [房永翠, 杨志安, 杨丽云 1932 物理学报 57 2661]
[23] Ma Y, Fu L B, Yang Z A 2006 Acta Phys. Sin. 55 5628 (in Chinese) [马云, 傅立斌, 杨志安 2006 物理学报 55 5628]
[24] Liu Z Z, Yang Z A 2007 Acta Phys. Sin. 56 1245 (in Chinese) [刘泽专, 杨志安 2007 物理学报 56 1245]
[25] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 物理学报 54 5003]
[26] Xu B, Ming N B 1994 Phys. Rev. A 50 5197
[27] Valkering T P, Irman A 2004 Phys. Rev. E 70 036610
[28] McAvity D M, Enns R H, Rangnekar S S 1988 Phys. Rev. A 38 4647
[29] Shchesnovich V S, Cavalcanti S B, Hickmann J M, Kivshar Y S 2006 Phys. Rev. E 74 056602
[30] Desyatnikov A S, Kivshar Y S, Shchesnovich V S, Cavalcanti S B, Hickmann J M 2007 Opt. Lett. 32 325
[31] Yosuke K, Yoshihiko M 2000 Phys. Rev. A 62 061401
[32] Yosuke K 1994 Phys. Rev. A 50 843
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[1] Ashkin A, Boyd G D, Dziedzic J M, Smith R G, Ballman A A, Levinstein J J, Nassau K 1966 Appl. Phys. Lett. 40 72
[2] Wang X D, Yu W L 2011 Acta Scientiarum Naturalium Universitatis Sunyatseni 40 32 (in Chinese) [王晓东, 佘卫龙 2011 中山大学学报: 自然科学版 40 32]
[3] Ren Z M 2005 Laser Journal 26 1 (in Chinese) [任占梅, 激光杂志 2005 26 1]
[4] Hou C F, Li S Q, Li F, Sun X D 2001 Progress In Physics 21 237 (in Chinese) [侯春风, 李师群, 李斌, 孙秀冬 2001 物理学进 21 237]
[5] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 3699 (in Chinese) [王沙, 杨志安 2009 物理学报 58 3699]
[6] Wang S, Yang Z A 2009 Acta Phys. Sin. 58 729 (in Chinese) [王沙, 杨志安 2009 物理学报 58 729]
[7] Hu Y, Lou C B, Liu S, Zhang P, Zhao J L, Xu J J, Chen Z G 2009 Opt. Lett. 34 1114
[8] Hu Y, Lou C B, Zhang P, Xu J J, Yang J K, Chen Z G 2009 Opt. Lett. 34 3259
[9] Zhang P, Liu S, Zhao J L, Lou C B, Xu J J, Chen Z G 2008 Opt. Lett. 33 878
[10] Chen S M, Shi S X, Dong H Z 2005 Acta Phys. Sin. 56 1379 (in Chinese) [陈守满, 石顺祥, 董洪舟 2005 物理学报 56 1379]
[11] Wang D S, Yu W L 2007 Acta Phys. Sin. 56 245 (in Chinese) [汪德生, 佘卫龙 2007 物理学报 56 245]
[12] Wang X S, Chen Z G, Wang J D, Yang J K 2007 Phys. Rev. Lett. 99 243901
[13] Ghulinyan M, Oton C J, Gaburro Z, Pavesi L T C, Wiersma D 2005 Phys. Rev. Lett. 94 127401
[14] Liu J, Fu L B 2010 Phys. Rev. A 81 1114
[15] Song D Y 2000 Phys. Rev. 85 1141
[16] Zhu S L, Wang Z D 2000 Phys. Rev. Lett. 85 1076
[17] Li S C, Liu J, Fu L B 2011 Phys. Rev. A 83 042107
[18] Wang G F, Liu F, Fu L B, Zhao H 2007 Acta Phys. Sin. 56 3733 (in Chinese) [王冠芳, 刘斌, 傅立斌, 赵鸿 2007 物理学报 56 3733]
[19] Ye D F, Fu L B, Zhao H, Liu J 2007 Acta Phys. Sin. 56 5071 (in Chinese) [叶地发, 傅立斌, 赵鸿, 刘杰 2007 物理学报 56 5071]
[20] Zener C 1932 Proc. R. Soc. London A 137 692
[21] Landau L 1932 Phys. Z. Sowjetunion 2 46
[22] Fang Y C, Yang Z A, Yang L Y 2008 Acta Phys. Sin. 57 2661 (in Chinese) [房永翠, 杨志安, 杨丽云 1932 物理学报 57 2661]
[23] Ma Y, Fu L B, Yang Z A 2006 Acta Phys. Sin. 55 5628 (in Chinese) [马云, 傅立斌, 杨志安 2006 物理学报 55 5628]
[24] Liu Z Z, Yang Z A 2007 Acta Phys. Sin. 56 1245 (in Chinese) [刘泽专, 杨志安 2007 物理学报 56 1245]
[25] Wang G F, Fu L B, Zhao H, Liu J 2005 Acta Phys. Sin. 54 5003 (in Chinese) [王冠芳, 傅立斌, 赵鸿, 刘杰 2005 物理学报 54 5003]
[26] Xu B, Ming N B 1994 Phys. Rev. A 50 5197
[27] Valkering T P, Irman A 2004 Phys. Rev. E 70 036610
[28] McAvity D M, Enns R H, Rangnekar S S 1988 Phys. Rev. A 38 4647
[29] Shchesnovich V S, Cavalcanti S B, Hickmann J M, Kivshar Y S 2006 Phys. Rev. E 74 056602
[30] Desyatnikov A S, Kivshar Y S, Shchesnovich V S, Cavalcanti S B, Hickmann J M 2007 Opt. Lett. 32 325
[31] Yosuke K, Yoshihiko M 2000 Phys. Rev. A 62 061401
[32] Yosuke K 1994 Phys. Rev. A 50 843
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